八大排序算法之归并排序

归并排序的核心是，每次将两个有序数组组合成为一个新的有序数组。对于俩个有序数组：

def merge(a:List[],b:List[])-->List[]:
    l_a,l_b = len(a),len(b)
    res = [0 for i in range(l_a+l_b)]
    index = 0
    i,j = 0,0
    while i<l_a or j<l_b:
        if a[i]<b[j]:
            res[index],index,i = a[i],index+1,i+1
        else:
            res[index],index,j = b[j],index+1,i+1
    while i<l_a:
        res[index],index,i = a[i],index+1,i+1
    while j<l_b:
        res[index],index,j = b[j],index+1,i+1

    return res

 归并排序中，两个有序数组是一段连续数组的俩部分：

#arr 传入数组，l,mid,r 传入数组的左边界，中间，右边界。l到mid与mid到r均有序，对l到r进行排序
def merge(arr,l,mid,r):
    hel = [0 for i in range(r-l+1)]
    i = 0
    p1,p2 = l,mid+1
    while p1<=mid and p2<=r:
        if arr[p1]<arr[p2]:
            hel[i],i,p1=arr[p1],i+1,p1+1
        else:
            hel[i],i,p2=arr[p2],i+1,p2+1
    while p1<=mid:
         hel[i],i,p1 = arr[p1],i+1,p1+1
    while p2<=r:
         hel[i],i,p2 = arr[p2],i+1,p2+1
    arr[l:r+1] = hel[:]

对于归并排序：

#归并排序，arr：排序数组 l：排序数组左边界，r：排序数组右边界。递归最深处的排序数组均为一个数字的数组，可以视为有序数组。
def sortProcess(arr,l,r):
    if l==r:
        return
    mid = (l+r>>1)
    sortProcess(arr,l,mid)
    sortProcess(arr,mid+1,r)
    merge(arr,l,mid,r)
def merge(arr,l,mid,r):
    hel = [0 for i in range(r-l+1)]
    i = 0
    p1,p2 = l,mid+1
    while p1<=mid and p2<=r:
        if arr[p1]<arr[p2]:
            hel[i],p1=arr[p1],p1+1
        else:
            hel[i],p2=arr[p2],p2+1
        i+=1
    while p1<=mid:
         hel[i],i,p1 = arr[p1],i+1,p1+1
    while p2<=r:
         hel[i],i,p2 = arr[p2],i+1,p2+1
    arr[l:r+1] = hel[:]

附上完整代码+对数器

import random

#size:数组长度
#end:范围
def getRandomArray(size,end,start=1):
    res = [random.randint(start,end) for i in range(size)]
    return res
def sortProcess(arr,l,r):
    if l==r:
        return
    mid = (l+r>>1)
    sortProcess(arr,l,mid)
    sortProcess(arr,mid+1,r)
    merge(arr,l,mid,r)
def merge(arr,l,mid,r):
    hel = [0 for i in range(r-l+1)]
    i = 0
    p1,p2 = l,mid+1
    while p1<=mid and p2<=r:
        if arr[p1]<arr[p2]:
            hel[i],p1=arr[p1],p1+1
        else:
            hel[i],p2=arr[p2],p2+1
        i+=1
    while p1<=mid:
         hel[i],i,p1 = arr[p1],i+1,p1+1
    while p2<=r:
         hel[i],i,p2 = arr[p2],i+1,p2+1
    arr[l:r+1] = hel[:]

nums = getRandomArray(20,15)
print(nums)
a = sorted(nums)
sortProcess(nums,0,len(nums)-1)
print(nums)
print(nums==a,'\n')

结果集：

[2, 1, 4, 10, 7, 5, 14, 1, 8, 2, 10, 10, 9, 15, 15, 12, 4, 2, 11, 3]
[1, 1, 2, 2, 2, 3, 4, 4, 5, 7, 8, 9, 10, 10, 10, 11, 12, 14, 15, 15]
True 

时间复杂度O(nlogn)，空间复杂度O(n)

同时，俩个数组合并的merge函数可以修改为：

def merge(arr,l,mid,r):
    hel = [0 for i in range(r-l+1)]
    i = 0
    p1,p2 = l,mid+1
    while p1<=mid and p2<=r:
        if arr[p1]<arr[p2]:
            hel[i],p1=arr[p1],p1+1
        else:
            hel[i],p2=arr[p2],p2+1
        i+=1
#     while p1<=mid:
#          hel[i],i,p1 = arr[p1],i+1,p1+1
    if p1<=mid:
        hel[i:] = arr[p1:mid+1]
        i = r-l+1
    arr[l:l+i] = hel[:i]

与原函数没有差距。